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Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .?
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Q. A convex lens forms a real and inverted image of a needle at a dist...
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Q. A convex lens forms a real and inverted image of a needle at a dist...
Given:
- Convex lens forms a real and inverted image of a needle
- Distance between the lens and image is 50 cm
- Size of the image is equal to the size of the object
To find:
- The position of the needle in front of the convex lens
- The power of the lens
Solution:
We know that the convex lens forms a real and inverted image of a needle. This indicates that the image is formed on the opposite side of the lens from where the object is placed.
Position of the needle:
Since the image formed is equal in size to the object, it indicates that the magnification produced by the lens is 1. We know that the magnification produced by a lens is given by the formula:
m = -v/u
Where m is the magnification, v is the distance between the lens and image, and u is the distance between the lens and object.
Since the magnification is 1, we can say that v = u. Hence, the distance between the lens and object is also 50 cm.
Power of the lens:
The power of the lens is given by the formula:
P = 1/f
Where P is the power of the lens and f is the focal length of the lens.
We know that the convex lens forms a real image of the object. Hence, the focal length of the lens is positive. The distance between the lens and image is given as 50 cm.
Using the lens formula, we can write:
1/f = 1/v - 1/u
Substituting the values, we get:
1/f = 1/50 - 1/50
Therefore, f = 50 cm.
Substituting the value of f in the formula for the power of the lens, we get:
P = 1/f = 1/50 = 0.02 dioptres
Therefore, the position of the needle in front of the convex lens is 50 cm and the power of the lens is 0.02 dioptres.
- Convex lens forms a real and inverted image of a needle
- Distance between the lens and image is 50 cm
- Size of the image is equal to the size of the object
To find:
- The position of the needle in front of the convex lens
- The power of the lens
Solution:
We know that the convex lens forms a real and inverted image of a needle. This indicates that the image is formed on the opposite side of the lens from where the object is placed.
Position of the needle:
Since the image formed is equal in size to the object, it indicates that the magnification produced by the lens is 1. We know that the magnification produced by a lens is given by the formula:
m = -v/u
Where m is the magnification, v is the distance between the lens and image, and u is the distance between the lens and object.
Since the magnification is 1, we can say that v = u. Hence, the distance between the lens and object is also 50 cm.
Power of the lens:
The power of the lens is given by the formula:
P = 1/f
Where P is the power of the lens and f is the focal length of the lens.
We know that the convex lens forms a real image of the object. Hence, the focal length of the lens is positive. The distance between the lens and image is given as 50 cm.
Using the lens formula, we can write:
1/f = 1/v - 1/u
Substituting the values, we get:
1/f = 1/50 - 1/50
Therefore, f = 50 cm.
Substituting the value of f in the formula for the power of the lens, we get:
P = 1/f = 1/50 = 0.02 dioptres
Therefore, the position of the needle in front of the convex lens is 50 cm and the power of the lens is 0.02 dioptres.
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Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .?
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Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .?.
Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it . Where is the needle placed in front of the convex lens if the image is equal to the size of the object ? Also , find the power of the lens .?.
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